When the weak separation condition implies the generalize finite type in $\mathbb{R}^d$

Abstract: Let $S$ be an iterated function system with full support. Under some restrictions on the allowable rotations, we will show that $S$ satisfies the weak separation condition if and only if it satisfies the generalized finite-type condition. To do this, we will extend the notion of net intervals from $\mathbb{R}$ to $\mathbb{R}^d$. If time allows, we will also use net intervals to calculate the local dimension of a self-similar measure with the finite-type condition and full support. This talk is based on joint work with Kevin G. Hare.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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